### Citations

5040 |
Stochastic relaxation, gibbs distributions, and the bayesian restoration of images
- Geman, Geman
- 1984
(Show Context)
Citation Context ...gularization models in [16]. The unifying theme of Bayesian modeling for low level problems appear for example, in [7, 2, 18]. A prototypical Bayesian formulation using MRF is that of Geman and Geman =-=[8]-=- for image restoration. Investigation of MRF modeling in high level vision such as object matching and recognition, which is more challenging (Introduction of [15]), begins only recently. In an initia... |

1606 |
Spatial interaction and the statistical analysis of lattice systems,”
- Besag
- 1974
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Citation Context ...alent to that conditioned on the events at the neighbors of i. It can be shown that the joint probability P (F = f) of any random field is uniquely determined by these local conditional probabilities =-=[1]-=-. However, it is usually difficult to specify the set of the conditional probabilities. Nonetheless, the Hammersley-Clifford theorem [1] of Markov-Gibbs equivalence provides a solution. According to t... |

887 | Visual Reconstruction.
- Blake, Zisserman
- 1987
(Show Context)
Citation Context ...upt changes in some properties in the direction tangent to the arc. The property can be the pixel value or directional derivatives of pixel value function. Continuous restoration with discontinuities =-=[8, 16, 3]-=- is a combination of LP1 and LP2. Volume B, pages 361--370, Stockholm, Sweden, May 1994. 5 Perceptual grouping [14] is an LP3. The sites usually correspond to initially segmented features (points, lin... |

525 |
Perceptual Organization and Visual Recognition,
- Lowe
- 1985
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Citation Context ...rivatives of pixel value function. Continuous restoration with discontinuities [8, 16, 3] is a combination of LP1 and LP2. Volume B, pages 361--370, Stockholm, Sweden, May 1994. 5 Perceptual grouping =-=[14]-=- is an LP3. The sites usually correspond to initially segmented features (points, lines and regions) which are inhomogeneously arranged. The fragmentary features are to be organized into perceptually ... |

286 |
Modeling and segmentation of noisy and textured images using Gibbs random fields
- Derin, Elliott
(Show Context)
Citation Context ...des a tool for analyzing spatial or contextual dependencies of physical phenomena. Define a neighborhood 6 In Proceedings of the European Conference on Computer Vision system for d N = fN i j 8i 2 dg =-=(6)-=- where N i is the collection of sites neighboring to i for which (1) i 62 N i and (2) i 2 N j () j 2 N i . The pair (d; N ) is a graph in the usual sense. A clique c for (d; N ) is a subset of d such ... |

268 | Constructing simple stable descriptions for image partitioning,”
- Leclerc
- 1989
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Citation Context ...ost due to the smoothness violation caused by f i \Gamma f j . For continuous restoration with discontinuities [8, 3], g(j) = min(j 2 ; ff). For piecewise constant reconstruction with discontinuities =-=[8, 9]-=-, g(j) = [1 \Gamma ffi(f i \Gamma f j )] where ffi(j) is the Dirichlet 8 In Proceedings of the European Conference on Computer Vision function. A general definition of g for discontinuity-adaptive res... |

227 |
Probabilistic solution of ill-posed problems in computational vision.
- Marroquin, Mitter, et al.
- 1987
(Show Context)
Citation Context ...ion and edge detection (There are a long list of references. Readers may refer to collections of papers in [15, 4] and references therein). Relationships between low level MRF models are discussed in =-=[16, 7]-=- and those between MRF models and regularization models in [16]. The unifying theme of Bayesian modeling for low level problems appear for example, in [7, 2, 18]. A prototypical Bayesian formulation u... |

202 | Bayesian Modeling of Uncertainty in Low-Level Vision.
- Szeliski
- 1989
(Show Context)
Citation Context ...een low level MRF models are discussed in [16, 7] and those between MRF models and regularization models in [16]. The unifying theme of Bayesian modeling for low level problems appear for example, in =-=[7, 2, 18]-=-. A prototypical Bayesian formulation using MRF is that of Geman and Geman [8] for image restoration. Investigation of MRF modeling in high level vision such as object matching and recognition, which ... |

138 |
Markov random fields : Theory and applications.
- Chellappa, Jain
- 1993
(Show Context)
Citation Context ...Among these are Markov Random Field (MRF) theory based models (of which analytic regularization theory based models are special cases). MRF modeling is appealing for the following reasons (Preface of =-=[4]-=-): (1) One can systematically develop algorithms based on sound principles rather than on some ad hoc heuristics for a variety of problems; (2) It makes it easier to derive quantitative performance me... |

120 |
Random field models in image analysis
- Dubes, Jain
- 1989
(Show Context)
Citation Context ...ion and edge detection (There are a long list of references. Readers may refer to collections of papers in [15, 4] and references therein). Relationships between low level MRF models are discussed in =-=[16, 7]-=- and those between MRF models and regularization models in [16]. The unifying theme of Bayesian modeling for low level problems appear for example, in [7, 2, 18]. A prototypical Bayesian formulation u... |

84 |
Towards Bayesian image analysis
- Besag
- 1989
(Show Context)
Citation Context ...een low level MRF models are discussed in [16, 7] and those between MRF models and regularization models in [16]. The unifying theme of Bayesian modeling for low level problems appear for example, in =-=[7, 2, 18]-=-. A prototypical Bayesian formulation using MRF is that of Geman and Geman [8] for image restoration. Investigation of MRF modeling in high level vision such as object matching and recognition, which ... |

50 |
A Markov Random Field Model-Based Approach to Image Interpretation
- Modestino, Zhang
- 1992
(Show Context)
Citation Context ...n high level vision such as object matching and recognition, which is more challenging (Introduction of [15]), begins only recently. In an initial development of an MRF model for image interpretation =-=[17]-=-, the optimal solution is defined as the MAP labeling. Unfortunately, the posterior probability therein is derived using heuristic rules instead of the laws of probability, which dissolves the origina... |

20 | A markov random field model for object matching under contextual constraints
- Li
- 1994
(Show Context)
Citation Context ...the laws of probability, which dissolves the original promises of MRF vision modeling. A coupled MRF network for simultaneous object recognition and segmentation is described in [5]. In a recent work =-=[11]-=-, an MRF model for high level object matching and recognition is formulated based on sound mathematical principles. Mathematically, like the typical low level MRF model of Geman and Geman [8], the mod... |

17 | Toward 3D vision from range images: An optimization framework and parallel networks
- Li
- 1992
(Show Context)
Citation Context ...r common mechanisms in seemingly different vision problems. It also suggests that these problems could be solved using a similar architecture. This paper presents such a unified MRF modeling approach =-=[10]-=-. The systematic way to the MRF modeling is summarized as five steps: 1. Pose the vision problem as one of labeling in which a label configuration represents a solution (Sec.2). 2. Further pose it as ... |

7 |
Parallel structure recognition with uncertainty: Coupled segmentation and matching
- Cooper
- 1990
(Show Context)
Citation Context ...stic rules instead of the laws of probability, which dissolves the original promises of MRF vision modeling. A coupled MRF network for simultaneous object recognition and segmentation is described in =-=[5]-=-. In a recent work [11], an MRF model for high level object matching and recognition is formulated based on sound mathematical principles. Mathematically, like the typical low level MRF model of Geman... |

2 |
On discontinuity adaptive regularization
- Li
(Show Context)
Citation Context ...i(f i \Gamma f j )] where ffi(j) is the Dirichlet 8 In Proceedings of the European Conference on Computer Vision function. A general definition of g for discontinuity-adaptive restoration is given in =-=[13]-=-. Geman and Geman [8] describe a general degraded image model based on which the likelihood function is obtained. In an important special case, each observed pixel value is assumed to be r i = f i +n ... |

1 |
Optimal selection of MRF parameters in object recognition
- Li
(Show Context)
Citation Context .... 7 with posterior energy E(f) = U(f j r) = U(f)=T + U(r j f) (11) Hence, given a fixed r, F is also an MRF on d with respect to N . The MAP solution is equivalently found by f = arg min f2S U(f j r) =-=(12)-=- To summarize, the MRF modeling process consists of the following steps: Defining a neighborhood system N , defining cliques C, defining the prior clique potentials, deriving the likelihood energy, an... |

1 |
Technical Editor. Special Issue on Statistic Image Analysis
- Mardia
- 1989
(Show Context)
Citation Context ...tation, surface reconstruction, texture analysis, optical flow, shape from X, visual integration and edge detection (There are a long list of references. Readers may refer to collections of papers in =-=[15, 4]-=- and references therein). Relationships between low level MRF models are discussed in [16, 7] and those between MRF models and regularization models in [16]. The unifying theme of Bayesian modeling fo... |